



'''simple docstring'''



def        UpperCAmelCase (    A	:					list[list]					):
							SCREAMING_SNAKE_CASE       :   List[str]         =      current_set.copy()
							for row_index, row in enumerate(A					):
														SCREAMING_SNAKE_CASE       :   List[Any]         =      row[0]
														for column_index, column in enumerate(A					):
																					if magnitude == 0:
																												SCREAMING_SNAKE_CASE       :   str         =      column
																												continue
																					SCREAMING_SNAKE_CASE       :   Optional[Any]         =      column / magnitude
    # Subtract to cancel term
							SCREAMING_SNAKE_CASE       :   List[Any]         =      current_set[0]
							SCREAMING_SNAKE_CASE       :   List[str]         =      [first_row]
							SCREAMING_SNAKE_CASE       :   int         =      current_set[1::]
							for row in current_set:
														SCREAMING_SNAKE_CASE       :   Union[str, Any]         =      []
														# If first term is 0, it is already in form we want, so we preserve it
														if row[0] == 0:
																					final_set.append(A					)
																					continue
														for column_index in range(len(A					)					):
																					temp_row.append(first_row[column_index] - row[column_index]					)
														final_set.append(A					)
							# Create next recursion iteration set
							if len(final_set[0]					) != 3:
														SCREAMING_SNAKE_CASE       :   Optional[Any]         =      final_set[0]
														SCREAMING_SNAKE_CASE       :   Any         =      []
														SCREAMING_SNAKE_CASE       :   str         =      []
														for row in final_set[1::]:
																					current_first_column.append(row[0]					)
																					next_iteration.append(row[1::]					)
														SCREAMING_SNAKE_CASE       :   str         =      simplify(A					)
														for i in range(len(A					)					):
																					resultant[i].insert(0       ,		current_first_column[i]					)
														resultant.insert(0       ,		A					)
														SCREAMING_SNAKE_CASE       :   Tuple         =      resultant
							return final_set
def        UpperCAmelCase (    A	:					list[list]					):
							if len(A					) == 0:
														raise IndexError('''solve_simultaneous() requires n lists of length n+1'''					)
							SCREAMING_SNAKE_CASE       :   Union[str, Any]         =      len(A					) + 1
							if any(len(A					) != _length for item in equations					):
														raise IndexError('''solve_simultaneous() requires n lists of length n+1'''					)
							for row in equations:
														if any(not isinstance(A       ,		(int, float)					) for column in row					):
																					raise ValueError('''solve_simultaneous() requires lists of integers'''					)
							if len(A					) == 1:
														return [equations[0][-1] / equations[0][0]]
							SCREAMING_SNAKE_CASE       :   Any         =      equations.copy()
							if any(0 in row for row in data_set					):
														SCREAMING_SNAKE_CASE       :   Union[str, Any]         =      data_set.copy()
														SCREAMING_SNAKE_CASE       :   List[str]         =      []
														for row_index, row in enumerate(A					):
																					if 0 not in row:
																												SCREAMING_SNAKE_CASE       :   Optional[int]         =      data_set.pop(A					)
																												break
														if not full_row:
																					raise ValueError('''solve_simultaneous() requires at least 1 full equation'''					)
														data_set.insert(0       ,		A					)
							SCREAMING_SNAKE_CASE       :   Union[str, Any]         =      data_set.copy()
							SCREAMING_SNAKE_CASE       :   Any         =      simplify(A					)
							SCREAMING_SNAKE_CASE       :   Any         =      simplified[::-1]
							SCREAMING_SNAKE_CASE       :   list         =      []
							for row in simplified:
														SCREAMING_SNAKE_CASE       :   List[Any]         =      row[-1]
														if not solutions:
																					if row[-2] == 0:
																												solutions.append(0					)
																												continue
																					solutions.append(current_solution / row[-2]					)
																					continue
														SCREAMING_SNAKE_CASE       :   int         =      row.copy()[: len(A					) - 1 :]
														while temp_row[0] == 0:
																					temp_row.pop(0					)
														if len(A					) == 0:
																					solutions.append(0					)
																					continue
														SCREAMING_SNAKE_CASE       :   Union[str, Any]         =      temp_row[1::]
														SCREAMING_SNAKE_CASE       :   List[Any]         =      temp_row[::-1]
														for column_index, column in enumerate(A					):
																					current_solution -= column * solutions[column_index]
														solutions.append(A					)
							SCREAMING_SNAKE_CASE       :   int         =      []
							for item in solutions:
														final.append(float(round(A       ,		5					)					)					)
							return final[::-1]


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							lowerCAmelCase_  :							Any             =    [
							    [2, 1, 1, 1, 1, 4],
							    [1, 2, 1, 1, 1, 5],
							    [1, 1, 2, 1, 1, 6],
							    [1, 1, 1, 2, 1, 7],
							    [1, 1, 1, 1, 2, 8],
							]
							print(solve_simultaneous(eq))
							print(solve_simultaneous([[4, 2]]))









'''simple docstring'''



import unittest

from transformers import is_tf_available
from transformers.testing_utils import require_tf


if is_tf_available():
							import tensorflow as tf
							from tensorflow.python.eager import context
							from tensorflow.python.framework import ops

							from transformers import GradientAccumulator, create_optimizer
@require_tf
class 						lowerCamelCase_				(       unittest.TestCase      ):







						def        __lowercase     (	self :   List[Any]					,     lowerCAmelCase__ :   str					,     lowerCAmelCase__ :   Dict					,     lowerCAmelCase__ :   int					):

													"""simple docstring"""
													self.assertEqual(len(lowerCAmelCase__					)					,     len(lowerCAmelCase__					)					)
													for a, b in zip(lowerCAmelCase__					,     lowerCAmelCase__					):
																				self.assertAlmostEqual(lowerCAmelCase__					,     lowerCAmelCase__					,     delta=lowerCAmelCase__					)







						def        __lowercase     (	self :   Dict					):

													"""simple docstring"""
													SCREAMING_SNAKE_CASE       :   List[Any]         =      GradientAccumulator()
													accumulator([tf.constant([1.0, 2.0]					)]					)
													accumulator([tf.constant([-2.0, 1.0]					)]					)
													accumulator([tf.constant([-1.0, 2.0]					)]					)
													with self.assertRaises(lowerCAmelCase__					):
																				accumulator([tf.constant([1.0, 1.0]					), tf.constant([2.0, 2.0]					)]					)
													self.assertEqual(accumulator.step					,     3					)
													self.assertEqual(len(accumulator.gradients					)					,     1					)
													self.assertListAlmostEqual(accumulator.gradients[0].numpy().tolist()					,     [-2.0, 5.0]					,     tol=1e-2					)
													accumulator.reset()
													self.assertEqual(accumulator.step					,     0					)
													self.assertListAlmostEqual(accumulator.gradients[0].numpy().tolist()					,     [0.0, 0.0]					,     tol=1e-2					)







						def        __lowercase     (	self :   List[str]					):

													"""simple docstring"""
													SCREAMING_SNAKE_CASE       :   Optional[int]         =      None
													ops.enable_eager_execution_internal()
													SCREAMING_SNAKE_CASE       :   List[Any]         =      tf.config.list_physical_devices('''CPU'''					)
													if len(lowerCAmelCase__					) == 1:
																				tf.config.set_logical_device_configuration(
																				    physical_devices[0]					,     [tf.config.LogicalDeviceConfiguration(), tf.config.LogicalDeviceConfiguration()]					)
													SCREAMING_SNAKE_CASE       :   Tuple         =      tf.config.list_logical_devices(device_type='''CPU'''					)
													SCREAMING_SNAKE_CASE       :   List[Any]         =      tf.distribute.MirroredStrategy(devices=devices[:2]					)

													with strategy.scope():
																				SCREAMING_SNAKE_CASE       :   Optional[Any]         =      GradientAccumulator()
																				SCREAMING_SNAKE_CASE       :   Dict         =      tf.Variable([4.0, 3.0]					)
																				SCREAMING_SNAKE_CASE       ,SCREAMING_SNAKE_CASE       :   Optional[int]         =      create_optimizer(5e-5					,     10					,     5					)
																				SCREAMING_SNAKE_CASE       :   List[Any]         =      tf.Variable([0.0, 0.0]					,     trainable=lowerCAmelCase__					)

													def accumulate_on_replica(lowerCAmelCase__ :   List[str]					):
																				accumulator([gradient]					)

													def apply_on_replica():
																				optimizer.apply_gradients(list(zip(accumulator.gradients					,     [variable]					)					)					)

													@tf.function
													def accumulate(lowerCAmelCase__ :   str					,     lowerCAmelCase__ :   List[Any]					):
																				with strategy.scope():
																											SCREAMING_SNAKE_CASE       :   Optional[Any]         =      strategy.experimental_local_results(lowerCAmelCase__					)
																											local_variables[0].assign(lowerCAmelCase__					)
																											local_variables[1].assign(lowerCAmelCase__					)
																											strategy.run(lowerCAmelCase__					,     args=(gradient_placeholder,)					)

													@tf.function
													def apply_grad():
																				with strategy.scope():
																											strategy.run(lowerCAmelCase__					)

													def _check_local_values(lowerCAmelCase__ :   Dict					,     lowerCAmelCase__ :   int					):
																				SCREAMING_SNAKE_CASE       :   Tuple         =      strategy.experimental_local_results(accumulator._gradients[0]					)
																				self.assertListAlmostEqual(values[0].value()					,     lowerCAmelCase__					,     tol=1e-2					)
																				self.assertListAlmostEqual(values[1].value()					,     lowerCAmelCase__					,     tol=1e-2					)

													accumulate([1.0, 2.0]					,     [-1.0, 1.0]					)
													accumulate([3.0, -1.0]					,     [-1.0, -1.0]					)
													accumulate([-2.0, 2.0]					,     [3.0, -2.0]					)
													self.assertEqual(accumulator.step					,     3					)
													_check_local_values([2.0, 3.0]					,     [1.0, -2.0]					)
													apply_grad()
													self.assertListAlmostEqual(variable.value()					,     [4.0, 3.0]					,     tol=1e-2					)
													accumulator.reset()
													self.assertEqual(accumulator.step					,     0					)
													_check_local_values([0.0, 0.0]					,     [0.0, 0.0]					)




